Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation

The nonlocal probabilistic theory developed in Part I is applied in numerical studies of plain concrete beams and is compared to the existing test data on the modulus of rupture. For normal size test beams, the deterministic theory is found to dominate and give adequate predictions for the mean. But the present probabilistic theory can further provide the standard deviation and the entire probability distribution (calculated via Latin hypercube sampling). For very large beam sizes, the statistical size effect dominates and the mean prediction approaches asymptotically the classical Weibull size effect. This is contrary to structures failing only after the formation of a large crack, for which the classical Weibull size effect is asymptotically approached for very small structure sizes. Comparison to the existing test data on the modulus of rupture demonstrates good agreement with both the measured means and the scatter breadth.